This is actually quite straight forward, as long as one knows where to look in the BRB. First off on page 104, "If a character has a cavalry mount, the whole model is treated as having the troop type cavalry and follows all the rules for both characters and cavalry models". So from this a scar vet cowboy is a cavalry model.
Moving on to page 97 - "..provided there is a friendly unit consisting of five or more models of the character's troop type within 3" " - So no 4+ look out sir for a saurus character on a cold one within 3" of any infantry unit (whether that is saurus, temple guard, chameleon skinks or skinks).
Page 99 - "If a character is hit by such an attack, and he is in a unit of at least 5 rank-and-file models (excluding champion, if there is one) and he is of the same troop type as the unit, then his controlling player is permitted to make a "Look Out Sir!" roll..." - So no 2+ Look Out Sir roll for a cowboy in an infantry unit either.
Following these rules Skink Characters on foot can have their usual 2+ Look Out Sir! rolls in any infantry unit and a 4+ if within 3" of an infantry unit.
There are no other rules regarding Look Out Sir! rolls, so there are no other instances in which you can make one.
I hope this helps!